Mathematical Morphology Operations Research Articles

An improved algorithm for detecting mesoscale ocean fronts from satellite observations: Detailed mapping of persistent fronts around the China Seas and their long-term trends

Mesoscale fronts are highly energetic ocean processes that dominate local biogeochemical processes and air-sea interactions and exert significant effects on ocean dynamics, ecology, and climate. An automatic front detection algorithm applied to satellite-based observations is a fundamental approach to acquiring frontal occurrence information. Histogram-based algorithms have been widely used in previous studies, and, despite being the most popular front detection algorithm, continuous improvements have been needed to address imperfect detection issues (undetected coastal fronts, discontinuities of fronts and repeated detection of fronts). In this study, a new algorithm is proposed to address the issues by coupling inverse distance weighting and mathematical morphology operators. Using 14,610 images acquired from 1982 to 2021, a series of comparisons between the new and existing algorithms have been implemented to validate the improvements. Statistical results suggest that the number of frontal pixels detected by our algorithm increased by 58.45% in the coastal domain when compared to previous methods. Statistical analysis also shows most of these increased fronts can be supported by a classic gradient-based method which is superior in detecting coastal fronts, which demonstrates the improvement of new algorithm in detecting coastal fronts. Furthermore, visual analyses suggest that our algorithm can better connect discontinuous fronts and reduce repeated detections, and statistical comparisons in the open seas present a 34.50% improvement in the average length of frontal segments. Moreover, based on an automated objective delineation method, an analysis of 40 years of seasonal frontal occurrences (as detected by our algorithm) produced a dataset that shows a detailed map of 59 persistent fronts around the China Seas. This map updates previously hand-delineated frontal positions and identifies some previously unreported persistent fronts. Further analyses show that the frontal occurrence or intensity of a majority of persistent fronts around the China Seas presents significant (P < 0.05) long-term variability over the last 40 years. The improved algorithm, together with its application in identifying persistent fronts around the China Seas, is expected to be extended to other waters to better investigate the response of marine ecosystems to front dynamics and predict the distribution of marine organisms within a changing climate.

Toward Efficient and Complete Line Segment Extraction for Large-Scale Point Clouds via Plane Segmentation and Projection

An efficient method based on plane segmentation and projection is proposed to extract as complete boundary (straight) line segments as possible. To efficiently detect boundary points, 3-D planar point clouds (patches) generated by plane segmentation are converted into 2-D images by graphical projection to avoid point-based nearest neighbors’ searching. To preserve boundary details, the projection resolution for each plane is determined through accurate statistics of average local intervals between points in voxels composing corresponding planar point clouds. To alleviate erroneous line segmentation extraction caused by uneven densities of planar point clouds, improved mathematical morphological operation, whose structural element order is self-adaptive to local point density, is proposed for crack inpainting of projected images. As for extraction of 3-D boundary line segments, the back-projection results of 2-D boundary line segments detected from images are utilized as references for clustering of boundary points, and a 3-D straight line fitting algorithm based on recursive weighted least squares is employed to reduce the effect of boundary noise. A series of refinement strategies are further presented to control the quality of extracted 3-D line segments. Experimental results demonstrate that the proposed line segment extraction method can provide efficient and fine processing results, as well as automatic processing ability, which satisfies the efficient processing demand for large-scale point clouds.

Morphological Operations on Unorganized Point Clouds Using Octree Graphs

Point clouds resulting from digital scanning are increasingly being used in the heritage field to create knowledge-based models, such as building information models (BIM) . Nevertheless, the use of digital image processing techniques in point cloud unorganized data is not well explored yet because of the lack of information about point adjacency and corresponding difficulty in structuring and manipulating data. In this study we propose an approach to deal with image processing-like mathematical morphological operations in unorganized point cloud using the octree graph. Our method consists of three main steps, namely: (i) computing the best distance value between points in the cloud; (ii) constructing an octree from point cloud; and (iii) producing a graph using rectangular layout. We exemplify the use of the proposed methodology performing morphological operations in grayscale and color point clouds of historical buildings. Results prove the effectiveness of the octree representation, which can efficiently generate an adjacency map, demonstrated by the resulting images, and has the potential to be applied at different areas of 3D data analysis.

End-to-end differentiable blind tip reconstruction for noisy atomic force microscopy images

Observing the structural dynamics of biomolecules is vital to deepening our understanding of biomolecular functions. High-speed (HS) atomic force microscopy (AFM) is a powerful method to measure biomolecular behavior at near physiological conditions. In the AFM, measured image profiles on a molecular surface are distorted by the tip shape through the interactions between the tip and molecule. Once the tip shape is known, AFM images can be approximately deconvolved to reconstruct the surface geometry of the sample molecule. Thus, knowing the correct tip shape is an important issue in the AFM image analysis. The blind tip reconstruction (BTR) method developed by Villarrubia (J Res Natl Inst Stand Technol 102:425, 1997) is an algorithm that estimates tip shape only from AFM images using mathematical morphology operators. While the BTR works perfectly for noise-free AFM images, the algorithm is susceptible to noise. To overcome this issue, we here propose an alternative BTR method, called end-to-end differentiable BTR, based on a modern machine learning approach. In the method, we introduce a loss function including a regularization term to prevent overfitting to noise, and the tip shape is optimized with automatic differentiation and backpropagations developed in deep learning frameworks. Using noisy pseudo-AFM images of myosin V motor domain as test cases, we show that our end-to-end differentiable BTR is robust against noise in AFM images. The method can also detect a double-tip shape and deconvolve doubled molecular images. Finally, application to real HS-AFM data of myosin V walking on an actin filament shows that the method can reconstruct the accurate surface geometry of actomyosin consistent with the structural model. Our method serves as a general post-processing for reconstructing hidden molecular surfaces from any AFM images. Codes are available at https://github.com/matsunagalab/differentiable_BTR.

Mathematical Morphology View of Topological Rough Sets and Its Applications

This article focuses on the relationship between mathematical morphology operations and rough sets, mainly based on the context of image retrieval and the basic image correspondence problem. Mathematical morphological procedures and set approximations in rough set theory have some clear parallels. Numerous initiatives have been made to connect rough sets with mathematical morphology. Numerous significant publications have been written in this field. Others attempt to show a direct connection between mathematical morphology and rough sets through relations, a pair of dual operations, and neighborhood systems. Rough sets are used to suggest a strategy to approximate mathematical morphology within the general paradigm of soft computing. A single framework is defined using a different technique that incorporates the key ideas of both rough sets and mathematical morphology. This paper examines rough set theory from the viewpoint of mathematical morphology to derive rough forms of the morphological structures of dilation, erosion, opening, and closing. These newly defined structures are applied to develop algorithm for the differential analysis of chest X-ray images from a COVID-19 patient with acute pneumonia and a health subject. The algorithm and rough morphological operations show promise for the delineation of lung occlusion in COVID-19 patients from chest X-rays. The foundations of mathematical morphology are covered in this article. After that, rough set theory ideas are taken into account, and their connections are examined. Finally, a suggested image retrieval application of the concepts from these two fields is provided.

Visualization and Characterization of Cumulative Arc Erosion Behavior Using 2-D Microscopic Images

The electrical arc erosion behavior extremely limits the lifespan of electromechanical switching devices. Observation of the gradual evolution of arc erosion is highly beneficial for to understand the arc ignition and the contact degradation. In this article, the erosion of contact materials is simulated and visualized in situ with the recorded 2-D microscopic images. A novel method for erosion area identification is proposed with the combination of difference image method and mathematical morphology operations. The variation in erosion area as a function of switching current cycles is demonstrated, and the center of erosion zone that migrates continuously during the endurance experiment is determined. Finally, not only three types of arc erosion regimes (centralized arc erosion, separated arc erosion, and commutated arc erosion) are revealed, but also the associated occurrence probabilities during 1000 cycles are provided.

РАЗРАБОТКА ВЫСОКОПРОИЗВОДИТЕЛЬНОГО МЕТОДА ОПРЕДЕЛЕНИЯ ГЕОМЕТРИЧЕСКИХ ПАРАМЕТРОВ ОБЪЕКТОВ НА ИЗОБРАЖЕНИИ

Currently, the development of various process automation systems is becoming more widelyused every day in various fields and industries, the task of developing software methods for thecorresponding automated systems remains urgent. One of the industries where the use and applicationof process automation systems is in demand is the field of non-contact measurement of objectsand their parameters. As an example, the task of determining the geometric parameters ofround timber stacked was chosen. In this regard, in this paper, methods were proposed for determiningthe geometric parameters of objects based on mathematical morphology operations, organizedusing the Canny detector and the Hough algorithm, and a method using a neural networkapproach based on the architecture of the YOLOv5 convolutional neural network. As a result ofthe conducted experimental studies, for the organization of which specially 3d-printed models oflogs were used, it was found that the method based on the use of neural networks is more accuratethan the method based on mathematical morphology. When solving the problem of counting thenumber of objects in the image, using the method based on the neural network approach, all objectslocated in the image were determined, whereas the method using mathematical morphology operations was able to determine only 13 of the 16 logs located, and I identified one false object,as a result of which the result error was about 19% for an image obtained from the Internet. Whenconducting an experiment on manufactured cylinder models, the method based on mathematicalmorphology operations showed unsatisfactory results. Another advantage of the method based onthe neural network approach is the possibility of calculating the area of the ends of logs in theimage and determining the volume of each of the logs located in the stack, as well as the total totalvolume of the entire pack of measured round timber.

An Approach for Counting Breeding Eels Using Mathematical Morphology Operations and Boundary Detection

Abstract The Mekong Delta region of Vietnam has great potential for agricultural development thanks to natural incentives. Many livestock industries have developed for a long time and play an important role in the country with many agricultural export products. In the era of breakthrough technologies and advances in information technology, many techniques are used to support the development of smart agriculture. In particular, computer vision techniques are widely applied to help farmers save a lot of labour and cost. This study presents an approach for counting eels based on Mathematical Morphology Operations and Boundary Detection from images of breeding eels captured with the proposed photo box. The proposed method is evaluated using data collected directly from a breeding eel farm in Vietnam. The authors of the research evaluate and investigate the length distribution of eels to select the appropriate size for counting tasks. The experiments show positive results with an average Mean Absolute Error of 2.2 over a tray of more than 17 eels. The contribution of the research is to provide tools to support farmers in eel farms to save time and effort and improve efficiency.

Genetic algorithm-based mathematical morphology for clutter removal in airborne radars

This paper presents a novel approach for clutter removal in airborne radars using a genetic algorithm and mathematical morphology. The clutter returns are detected when constant alarm rate processing is applied on range-Doppler images. In the proposed method, mathematical morphological operations are performed on range-Doppler images to obtain clutter images. The clutter image is then applied as a mask to remove false detections due to clutter. Also, the targets embedded in clutter are detected using gray-scale morphological operations. The morphological filter and the sequence of operations are designed by a genetic algorithm. The advantage of the proposed method is that it does not require the computation of statistical measures from clutter data and filters are optimally designed using a genetic algorithm. The proposed method has shown an increase in clutter leak reduction when compared to that of a deep morphological network.

Improving performance of deep learning models using 3.5D U-Net via majority voting for tooth segmentation on cone beam computed tomography

Deep learning allows automatic segmentation of teeth on cone beam computed tomography (CBCT). However, the segmentation performance of deep learning varies among different training strategies. Our aim was to propose a 3.5D U-Net to improve the performance of the U-Net in segmenting teeth on CBCT. This study retrospectively enrolled 24 patients who received CBCT. Five U-Nets, including 2Da U-Net, 2Dc U-Net, 2Ds U-Net, 2.5Da U-Net, 3D U-Net, were trained to segment the teeth. Four additional U-Nets, including 2.5Dv U-Net, 3.5Dv5 U-Net, 3.5Dv4 U-Net, and 3.5Dv3 U-Net, were obtained using majority voting. Mathematical morphology operations including erosion and dilation (E&D) were applied to remove diminutive noise speckles. Segmentation performance was evaluated by fourfold cross validation using Dice similarity coefficient (DSC), accuracy, sensitivity, specificity, positive predictive value (PPV), negative predictive value (NPV). Kruskal–Wallis test with post hoc analysis using Bonferroni correction was used for group comparison. P < 0.05 was considered statistically significant. Performance of U-Nets significantly varies among different training strategies for teeth segmentation on CBCT (P < 0.05). The 3.5Dv5 U-Net and 2.5Dv U-Net showed DSC and PPV significantly higher than any of five originally trained U-Nets (all P < 0.05). E&D significantly improved the DSC, accuracy, specificity, and PPV (all P < 0.005). The 3.5Dv5 U-Net achieved highest DSC and accuracy among all U-Nets. The segmentation performance of the U-Net can be improved by majority voting and E&D. Overall speaking, the 3.5Dv5 U-Net achieved the best segmentation performance among all U-Nets.

Automatic bone segmentation for oral surgical planning

Introduction: Evolvement of digital technology encouraged the use of virtual dental and dental surgical planning and navigated surgery. The variety of cases is significant, therefore even for an expert, it is challanging to recover a traumatic case, or to design and apply implants with high anatomical precision. Objective: High-quality image acquisition and processing are essential to the process. CT (computer tomography) or CBCT (cone-beam computer tomography) images having bad initial quality greatly decrease the performance of the processing algorithms and affect the quality of the reconstructed 3D models. 3D reconstruction using manual segmentation takes several hours of work and expertise, which significantly increases the overall cost and time of 3D CAD/CAM (computer-aided design/computer-aided manufacturing) based surgical planning and production processes. Material and method: In this paper, we introduce a bone segmentation algorithm specifically designed for surgical planning, and evaluate its benefits for the aforementioned goal. The approach relies on edge detection, mathematical morphology and basic image-processing operations. Results: Performance has been evaluated on 40 series of manual segmentation. Results (precision 90%) show that the algorithm is fast and accurate so it is applicable for surgical planning. Conclusion: Our algorithm significantly reduces the execution time of segmentation and surgical planning, therefore increases the efficiency of the overall procedure.

Research on mathematical morphological operators for fault diagnosis of rolling element bearings

Morphological filtering adopting the combined morphological operators (CMOs) has been widely used to extract bearing fault features from vibration signals. However, few studies focus on the comprehensive performance of various CMOs under different interferences. In this paper, several new CMOs for feature extraction are proposed firstly, and then the impulse extraction performance of fourteen typical CMOs in the presence of harmonic interference, random impulses and background noise is investigated through simulations. To enhance the capability of impulse extraction and noise elimination, the morphological hat cross-correlation operator (MHCCO) is constructed through the cross-correlation of two CMOs with excellent performance. Additionally, an improved strategy is proposed to adaptively determine the optimal length of the structural element for MHCCO. Simulations, experiments and comparisons demonstrate the effectiveness and superiority of the proposed method. This paper provides important guidance for selecting CMO for feature extraction and an effective method for bearing fault diagnosis.

Diabetic foot ulcer segmentation using logistic regression, DBSCAN clustering and mathematical morphology operators

Digital images are used for evaluation and diagnosis of a diabetic foot ulcer. Selecting the wound region (segmentation) in an image is a preliminary step for subsequent analysis. Most of the time, manual segmentation isn't very reliable because specialists could have different opinions over the ulcer border. This fact encourages researchers to find and test different automatic segmentation techniques. This paper presents a computer-aided ulcer region segmentation algorithm for diabetic foot images. The proposed algorithm has two stages: ulcer region segmentation, and post-processing of segmentation results. For the first stage, a trained machine learning model was selected to classify pixels inside the ulcer's region, after a comparison of five learning models. Exhaustive experiments have been performed with our own annotated dataset from images of Cuban patients. The second stage is needed because of the presence of some misclassified pixels. To solve this, we applied the DBSCAN clustering algorithm, together with dilation, and closing morphological operators. The best-trained model after the post-processing stage was the logistic regressor (Jaccard Index $0.81$, accuracy $0.94$, recall $0.86$, precision $0.91$, and F1 score $0.88$). The trained model was sensitive to irrelevant objects in the scene, but the patient foot. Physicians found these results promising to measure the lesion area and to follow-up the ulcer healing process over treatments, reducing errors.

MORPHOLOGICAL SPATIAL PATTERN ANALYSIS: OPEN SOURCE RELEASE

Abstract. The morphological segmentation of binary patterns provides an effective method for characterising spatial patterns with emphasis on connections between their parts as measured at varying analysis scales. The method is widely used for the analysis of landscape patterns such as those related to the fragmentation of forests or other natural land cover classes. This can be explained by its effectiveness at capturing the complexity of binary patterns and their connections by partitioning the foreground pixels of the corresponding binary images into mutually exclusive classes. While the principles of the method are conceptually simple, the definition of the classes relies on a series of advanced mathematical morphology operations whose actual implementation is not straightforward. In this paper, we propose an open source code for MSPA and detail its main components in the form of pseudo-code. We demonstrate its effectiveness for asynchronous processing of tera-pixel images and the synchronous exploratory analysis and rendering with Jupyter notebooks.

Optimization in Mathematics Modeling and Processing of New Type Silicate Glass Ceramics

Abstract This paper applies the Gaussian random field to the mathematical modeling of new-type silicate glass-ceramic trachoma detection. The article established a three-dimensional numerical model of trachoma structure based on the anisotropic random field. Then, the open and closed operations in mathematical morphology are used to obtain the strongly connected boundaries of the new-type silicate glass-ceramic trachoma image. At the same time, the connected domain detection in binary morphology is used to remove the noise to obtain the target image of the silicate glass-ceramic pore. The study found that this method can better meet the requirements of silicate glass-ceramic trachoma measurement than the classic edge detection operator.

An Improved Data-Efficiency Algorithm Based on Combining Isolation Forest and Mean Shift for Anomaly Data Filtering in Wind Power Curve

A wind turbine working in a harsh environment is prone to generate abnormal data. An efficient algorithm based on the combination of an Isolation Forest (I-Forest) and a mean-shift algorithm is proposed for data cleaning in wind power curves. The I-Forest is used for detecting the local anomalies in each power and wind speed interval after data preprocessing. The contamination of I-Forest can be flexibly adjusted according to the data distribution of the wind turbine data. The remaining stacked data is eliminated by the mean-shift algorithm. To verify the filtering performance of the proposed combined method, five different algorithms, including the quartile and k-means (QK), the quartile and density-based spatial clustering (QD), the mathematical morphology operation (MMO), the fast data cleaning algorithm (FA), and the proposed one, are applied to the wind power curves of a prototype wind farm for comparisons. The numerical results have positively confirmed the reliability of the universal framework provided by the proposed algorithm.

Detection of Lung Cancer using Computed Tomography CT-Scan Images

Cancer is one of the most serious and widespread disease that is responsible for large number of deaths every year. Among all different types of cancers, lung cancer is the most prevalent cancer having the highest mortality rate. Computed tomography scans are used for identification of lung cancer as it provides detailed picture of tumor in the body and tracks its growth. Computed Tomography is preferred over other imaging modalities, visual interpretation of these CT scan images may be an error prone task and can cause delay in lung cancer detection. The algorithm for lung cancer detection is proposed using methods such as median filtering for image preprocessing followed by segmentation of lung region of interest using mathematical morphological operations.

IMPROVING LOCAL ADAPTIVE FILTERING METHOD EMPLOYED IN RADIOMETRIC CORRECTION OF ANALOGUE AIRBORNE CAMPAIGNS

Abstract. An orthophotomosaic is as a single image that can be layered on a map. It is produced from a set of aerial images impaired by radiometric inhomogeneity mostly due to atmospheric phenomena, like hotspot, haze or high altitude clouds shadows as well as the camera itself, like lens vignetting. These create some unsightly radiometric inhomogeneity in the mosaic that could be corrected by using a local adaptive filter, also named Wallis filter. Yet this solution leads to a significant loss of contrast at small scales. This current work introduces two elementary studies. In a first time, in order to quantify the loss of contrast due to the use of Wallis filter, a simple multi-scale score is proposed based on mathematical morphology operations. In a second time, an optimal window size for the filter is identified by considering some systematic radiometric behaviours in the images forming the mosaic through Principal Component Analysis (PCA). These two elementary studies are preliminary steps leading to a method of radiometric correction combining Wallis filtering and PCA.

K-MEANS CLUSTERING BASED ON OMNIVARIANCE ATTRIBUTE FOR BUILDING DETECTION FROM AIRBORNE LIDAR DATA

Abstract. Building detection is an important process in urban applications. In the last decades, 3D point clouds derived from airborne LiDAR have been widely explored. In this paper, we propose a building detection method based on K-means clustering and the omnivariance attribute derived from eigenvalues. The main contributions lie on the automatic detection without the need for training and optimal neighborhood definition for local attribute estimation. Additionally, one refinement step based on mathematical morphology (MM) operators to minimize the classification errors (commission and omission errors) is proposed. The experiments were conducted in three study areas. In general, the results indicated the potential of proposed method, presenting an average Fscore around 97%.

Brain Extraction in Multiple T1-weighted Magnetic Resonance Imaging slices using Digital Image Processing techniques

Brain Imaging has been source of several studies in the literature, mostly due to its importanceboth to predict and to analyze certain diseases or conditions. Extracting the brain from patient images for medical analysis can provide useful diagnostic and prognostic information.To this end, digital image processing algorithms have been applied to medical tasks with a focus on the identification of the brain. This work proposes a brain extraction framework based on three major steps: 1) Dataset and Image Selection; 2) Preprocessing; and 3) Largest Connected Component extraction. Our data are obtained from the OASIS dataset.The preprocessing step is applied in order to enhance contrast and eliminate possible noise from the T1-weighted MRI. Largest Connected Component extraction is performed by initially detecting the largest element in the image (i.e. the brain gray matter) and then by extracting it through mathematical morphology operators. The unsupervised framework extracts the brain in different axial slices without adjustments. The main contribution of this work is a method using only digital image processing for automatically identifying the brain from several different slices, which differs from the literature since is performed without parameter resetting. Five metrics were applied to evaluate our results: Specificity, Recall, Accuracy, F-Measure, and Precision. In our first experiment, two metrics resulted in more than 90% in efficiency (Specificity and Precision), two of them surpassed 80% (F-Measure and Accuracy), and Sensitivity exceeded 70%. Our second experiment compares our results with those produced by related works, having been ranked in the top positions of Sensitivity and Specificity.